Problem 1 :
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?
Let the trains meet each other "m" hours after 7 a.m.
Distance covered by the train from A in "m" hrs is
= Speed ⋅ Time
= 20 kms
At a particular time after 8 a.m, if the train from A had traveled "m" hours, then the train from B would have traveled (m-1) hours.
Because it started at 8.00 am. (one hour later)
Distance covered by the train from B in (m - 1) hrs is
= 25(m - 1)
At the meeting point,
sum of the distances covered by the two trains is equal to the total distance (from A to B).
20m + 25(m-1) = 110
20m + 25m - 25 = 110
45m = 135
m = 3 hours
So, two trains meet each other 3 hrs after 7 a.m
That is, at 10 a.m.
Hence, the time at which they will meet is 10 a.m.
Problem 2 :
Two trains are running at 40 kmph and 20 kmph respectively in the same direction .Faster train completely passes a man who is sitting in the slower train in 9 seconds. What is the length of the faster train?
Relative speed of two trains is
= 40 - 20
= 20 kmph
= 20 ⋅ 5/18 m/sec
= 50/9 m/sec
Given : Faster train completely passes a man who is sitting in the slower train in 9 seconds.
Length of the faster train is
= The distance covered by the faster train in this 9 seconds
= Speed ⋅ Time
= 50/9 ⋅ 9
= 50 m
Hence, the length of the faster train is 50 m.
Problem 3 :
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. Find the ratio of their speeds
Let "a" m/sec and "b" m/sec be the speeds of two trains respectively
First train crosses the man in 27 seconds with speed "a" m/sec
So, the length of the first train is
= Distance covered in 27 seconds
= Speed ⋅ Time
= a ⋅ 27
= 27a -----(1)
Second train crosses the man in 17 seconds with speed "b" m/sec
Length of the second train is
= Distance covered in 17 seconds
= Speed ⋅ Time
= b ⋅ 17
= 17b -----(2)
Given : The given two trains cross each other in 23 seconds.
The distance covered by the two trains in this 23 seconds is
= Sum of the lengths of the two trains
= Relative speed ⋅ Time
= (a + b) ⋅ 23
= 23a + 23b -----(3)
We know the fact that when two trains cross each other in opposite directions, the distance covered by them is equal to sum of the length of the two trains.
(1) + (2) = (3)
27a + 17b = 23a + 23b
4a = 6b
a / b = 6 / 4
a / b = 3 / 2
a : b = 3 : 2
Hence, the ratio of their speeds is 3:2.
Problem 4 :
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?
Speed of the train = 54 kmph
= 54 ⋅ 5/18 m/sec
= 15 m/sec
The train passes the man in 20 seconds.
The distance covered by the train in this 20 seconds is equal to the length of the train.
Distance = Speed ⋅ Time
Distance = 20 ⋅ 15
Distance = 300 m
So, length of the train is 300 m.
Let "m" be the length of the platform
Given : The train crosses the platform in 36 seconds.
We know the fact that the distance covered by the train in this 36 seconds is equal to sum of the lengths of the train and platform
Then, the distance covered by the train in 36 seconds is
= 300 + m
So, the train takes 36 seconds to cover the distance "300 + m"
Time = Distance / Speed
36 = (300 + m) / 15
540 = 300 + m
240 = m
Hence, the length of the platform is 240 meters.
Problem 5 :
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. Find the time taken by the two trains to cross each other.
Relative speed is
= 60 + 90 = 150 kmphr
= 150 ⋅ 5/18 m/sec
= 125/3 m/sec
When they cross each other, distance covered by both the trains is equal to sum of the lengths of the two trains.
So, the distance covered by them is
= 1.1 + 0.9
= 2 km
= 2 ⋅ 1000 m
= 2000 m
Time taken by the two trains to cross each other is
= Distance / Speed
= 2000 / (125/3)
= 2000 ⋅ 3/125
= 48 seconds
Hence, time taken by the two trains to cross each other is 48 seconds.
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